「17平均律」の版間の差分

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'''17平均律'''はオクターブを均等に17分割したものであり、各ステップは70.588[[セント|セント]]である。13平均律に次ぎ19平均律の前となる、7番目の素数平均律である。
'''17平均律'''はオクターブを均等に17分割したものであり、各ステップは約 70.588 [[セント|¢]] である。13平均律に次ぎ19平均律の前となる、7番目の素数平均律である。


==17平均律の音程と近似値==
==17平均律の音程と近似値==
342行目: 342行目:


平均律は2.3.25.7.11.13サブグループテンペラメントとしてもっともらしく扱うことができる。それはとても計算されている。7リミット周波数比は一般的に、他の整数と同じぐらい良く現れないけども。
平均律は2.3.25.7.11.13サブグループテンペラメントとしてもっともらしく扱うことができる。それはとても計算されている。7リミット周波数比は一般的に、他の整数と同じぐらい良く現れないけども。
===素数倍音===
{{harmonics in equal|17}}
==純正音程近似==
===純正音程のマッピング===
{{q-odd-limit intervals|17}}


==コンマをなだらかにする==
==コンマをなだらかにする==
17平均律を< 17 27 39 48 59 63 |[[ヴァル|ヴァル]]とみなした時、次のリストのコンマをテンパーアウトする。
17平均律の[[ヴァル]]を {{val|17 27 39 48 59 63}} とみなした時、次のリストのコンマをテンパーアウトする。


{| class="wikitable"
{| class="wikitable"
443行目: 450行目:


==Scales==
==Scales==
* [[17平均律律テトラコード]]
<ul><li>[[Otonal_17|Otonal 17]]</li><li>[http://www.microtonalismo.com/proyecto-xvii Blues Peruvian 17edo]</li><li>[[17edo_neutral_scale|17edo neutral scale]]</li><li>[[Scorp|Scorp]]</li><li>[[MOS_scales_of_17edo|MOS scales of 17edo]] (horograms)</li></ul>
<ul><li>[[Otonal_17|Otonal 17]]</li><li>[http://www.microtonalismo.com/proyecto-xvii Blues Peruvian 17edo]</li><li>[[17edo_neutral_scale|17edo neutral scale]]</li><li>[[Scorp|Scorp]]</li><li>[[MOS_scales_of_17edo|MOS scales of 17edo]] (horograms)</li></ul>


456行目: 464行目:
===Sound files===
===Sound files===
<ul><li><span style="">''[https://soundcloud.com/aaron-krister-johnson/puhlops-and-lauguas-big-adventure Puhlops and Laugua's Big Adventure]'' </span> by [http://www.untwelve.org/board |Aaron Krister Johnson]</li><li><span style="">''[https://soundcloud.com/aaron-krister-johnson/adagio-for-margo Adagio for Margo]'' </span> by [http://www.untwelve.org/board Aaron Krister Johnson]</li><li><span style="">''[http://home.comcast.net/%7Eteamouse/Transformation.mp3 Transformation]'' </span> by [http://home.comcast.net/%7Eteamouse/ Herman Miller]</li><li><span style="">''[http://www.emcollective.org/chris/items/17tet/17waltz.mp3 Waltz]'' </span> by Christopher Bailey</li><li><span style="">''[http://www.emcollective.org/chris/items/17Chorus/17tppp4_lostfound.mp3 Lostfound]'' </span> by Christopher Bailey</li><li>excerpt from <span style="">''[http://music.columbia.edu/%7Echris/sounds/balladei_exc.mp3 Balladei]'' </span> (in 17, 29 and 12) by [http://music.columbia.edu/%7Echris/ Christopher Bailey] , CD available [http://www.amazon.com/Christopher-Bailey-Shiau-Uen-Jacob-Rhodebeck/dp/B000TDZSAU/ref=sr_1_19/105-0183009-3913216?ie=UTF8&s=music&qid=1184598550&sr=1-19 here] .</li><li><span style="">''[http://www.h-pi.com/mp3/17ET.mp3 Two-Part Invention in 17ET]'' </span> by Aaron Andrew Hunt</li><li>''[http://micro.soonlabel.com/gene_ward_smith/Others/McGowan/MSND-Ovtr.mp3 Overture to A Midsummer Night's Dream]'' by [http://azuma-asobi.com/ Rick McGowan]</li><li>''[http://micro.soonlabel.com/gene_ward_smith/Others/McGowan/FairyLullaby-1.mp3 Fairy Lullaby from A Midsummer Night's Dream]'' by [http://azuma-asobi.com/ Rick McGowan]</li><li><span style="">''[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2017-A%20Calamitous%20Simultaneity.mp3 A Calamitous Simultaneity]'' </span> by Igliashon Jones (17edo and 22edo)</li><li><span style="">''[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/First%20Impressions.mp3 First Impressions]'' </span> by Igliashon Jones</li><li>[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/I%20Insist.mp3 I Insist] by Igliashon Jones</li><li>''[http://archive.org/download/EtudeNo1For2PianosIn17EqualTemperament/EtudeForTwoPianosIn17edo.mp3 Etude no1 for 2 Pianos in 17 Equal Temperament]'' and ''[http://archive.org/download/EtudeNo2For2PianosIn17EqualTemperament/EtudeNo2ForTwoPianosIn17edo.mp3 Etude no2 for 2 Pianos in 17 Equal Temperament]'' Jon Lyle Smith</li><li>A number of compositions from [http://www.archive.org/details/seventeenTPP_01 seventeen-tone piano project phase I] , [[SeventeenTPPPhaseTwo|seventeen-tone piano project phase II]], [[SeventeenTPPPhaseThree|seventeen-tone piano project phase III]].</li><li>[http://www.archive.org/search.php?query=subject%3A%2217-edo%22 17edo] - 17edo-tagged compositions on www.archive.org</li><li>[http://soundclick.com/share?songid=8839072 sing a blue] by Andrew Heathwaite (composed 2008, recorded 2010). This and the other pieces below by Andrew for cümbüş, steel tubes &amp; voice.</li><li>[http://soundclick.com/share?songid=8839073 stringfinger it everybean] by Andrew Heathwaite (composed 2008, recorded 2010).</li><li>[http://soundclick.com/share?songid=8839069 cat feet belly] by Andrew Heathwaite (composed 2008, recorded 2010).</li><li><span style="">''[http://www.youtube.com/watch?v=a9N_T6LNDaE 17 Tone Jam]'' </span> by Marmalade Man</li><li>[http://www.youtube.com/results?search_query=17edo&search=tag youtube videos tagged with 17edo]</li><li>[http://chrisvaisvil.com/?p=784 On the Shores of the Dead Sea blog] <span style="">''[http://www.youtube.com/watch?v=D39MVFhb0Ho video of On the Shores of the Dead Sea]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=466 Only in Disneyland 17 blog] edo guitar solo <span style="">''[http://micro.soonlabel.com/17-ET/daily20110205-17et-disneyland.mp3 play Only in Disneyland]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=460 17 Reasons I Hate the Blues blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110125b-17-reasons-I-hate-the-blues.mp3 play 17 Reasons I Hate the Blues]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=422 Klingon Opera Overture blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110109-albino-17et.mp3 play Klingon Opera Overture]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=298 Seventeen Selfless Notes blog] <span style="">''[http://micro.soonlabel.com/17-ET/if20101028selfless.mp3 play Seventeen Selfless Notes]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=76 17ET Jazz blog] <span style="">''[http://micro.soonlabel.com/17-ET/60x60-4001-1-ver2.mp3 play 17et Jazz]'' </span> by Chris Vaisvil (60 x 60 winner)</li><li>[http://chrisvaisvil.com/?p=742 17 Pink Tuxedos blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110416-17_pink-tuxes.mp3 play 17 Pink Tuxedos]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=706 Devil in the Deep Blue Sea blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110401-17-2-devil_in_the_deep_blue_sea.mp3 play Devil in the Deep Blue sea]'' </span> blues collaboration between The Two Regs (vocals / lyrics) and Norm Harris (percussion) and Chris Vaisvil (17 note per octave electric guitar and fretless bass).</li><li>[http://chrisvaisvil.com/?p=585 Seventeen Years in the Sixties blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110318-seventeen-years-in-the-sixties.mp3 play Seventeen Years in the Sixties]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=699 CT Scan blog] <span style="">''[http://www.youtube.com/watch?v=ZEEuytYwtbo play video CT Scan]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=470 Fish and a Grenade blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110208-17-a-fish-and-a-grenade.mp3 play Fish and a Grenade]'' </span> (parental advisory language) by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=550 Seventeen Unsteady Hands blog] <span style="">''[http://www.youtube.com/watch?v=rAKHCqBNhfc play video of performance of Seventeen Unsteady Hands]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=38 The Pond blog] by Chris Vaisvil and <span style="">''[http://www.youtube.com/watch?v=25sC3_uheyA video version of The Pond with Japanese Garden ]'' </span></li><li><span style="">[http://chrisvaisvil.com/?p=305 Graveyard blog] </span><span style="">''[http://micro.soonlabel.com/17-ET/if20101028-graveyard.mp3 play Graveyard]'' </span> by Chris Vaisvil</li><li><span style="">''[http://micro.soonlabel.com/17-ET/daily20110713_q49_17_brass_voice_choirs.mp3 For Brass and Voice Choirs in 17 edo]'' </span> by [http://chrisvaisvil.com/ Chris Vaisvil ] [http://chrisvaisvil.com/?p=1039 more on the composition]</li><li><span style="">''[http://micro.soonlabel.com/17-ET/daily20111015-fungi.mp3 And I Became One With My Per Fungi]'' </span> by [http://chrisvaisvil.com/ Chris Vaisvil] =&gt; [http://chrisvaisvil.com/?p=1439 more on composition]</li><li><span style="">''[http://micro.soonlabel.com/17-ET/20111014-STE-002-counter-intuitive.mp3 counterintuitive (17 edo guitar solo)]'' </span> by [http://www.chrisvaisvil.com/ Chris Vaisvil] =&gt; [http://chrisvaisvil.com/?p=1427 more on composition]</li><li>[http://micro.soonlabel.com/gene_ward_smith/Others/Sanchez/No_Love_by_Gregory_Sanchez_1_on_SoundCloud___Hear_the_world_s_sounds.mp3 No Love] by [https://soundcloud.com/gregory-sanchez-2/no-love Gregory Sanchez]</li></ul>
<ul><li><span style="">''[https://soundcloud.com/aaron-krister-johnson/puhlops-and-lauguas-big-adventure Puhlops and Laugua's Big Adventure]'' </span> by [http://www.untwelve.org/board |Aaron Krister Johnson]</li><li><span style="">''[https://soundcloud.com/aaron-krister-johnson/adagio-for-margo Adagio for Margo]'' </span> by [http://www.untwelve.org/board Aaron Krister Johnson]</li><li><span style="">''[http://home.comcast.net/%7Eteamouse/Transformation.mp3 Transformation]'' </span> by [http://home.comcast.net/%7Eteamouse/ Herman Miller]</li><li><span style="">''[http://www.emcollective.org/chris/items/17tet/17waltz.mp3 Waltz]'' </span> by Christopher Bailey</li><li><span style="">''[http://www.emcollective.org/chris/items/17Chorus/17tppp4_lostfound.mp3 Lostfound]'' </span> by Christopher Bailey</li><li>excerpt from <span style="">''[http://music.columbia.edu/%7Echris/sounds/balladei_exc.mp3 Balladei]'' </span> (in 17, 29 and 12) by [http://music.columbia.edu/%7Echris/ Christopher Bailey] , CD available [http://www.amazon.com/Christopher-Bailey-Shiau-Uen-Jacob-Rhodebeck/dp/B000TDZSAU/ref=sr_1_19/105-0183009-3913216?ie=UTF8&s=music&qid=1184598550&sr=1-19 here] .</li><li><span style="">''[http://www.h-pi.com/mp3/17ET.mp3 Two-Part Invention in 17ET]'' </span> by Aaron Andrew Hunt</li><li>''[http://micro.soonlabel.com/gene_ward_smith/Others/McGowan/MSND-Ovtr.mp3 Overture to A Midsummer Night's Dream]'' by [http://azuma-asobi.com/ Rick McGowan]</li><li>''[http://micro.soonlabel.com/gene_ward_smith/Others/McGowan/FairyLullaby-1.mp3 Fairy Lullaby from A Midsummer Night's Dream]'' by [http://azuma-asobi.com/ Rick McGowan]</li><li><span style="">''[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2017-A%20Calamitous%20Simultaneity.mp3 A Calamitous Simultaneity]'' </span> by Igliashon Jones (17edo and 22edo)</li><li><span style="">''[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/First%20Impressions.mp3 First Impressions]'' </span> by Igliashon Jones</li><li>[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/I%20Insist.mp3 I Insist] by Igliashon Jones</li><li>''[http://archive.org/download/EtudeNo1For2PianosIn17EqualTemperament/EtudeForTwoPianosIn17edo.mp3 Etude no1 for 2 Pianos in 17 Equal Temperament]'' and ''[http://archive.org/download/EtudeNo2For2PianosIn17EqualTemperament/EtudeNo2ForTwoPianosIn17edo.mp3 Etude no2 for 2 Pianos in 17 Equal Temperament]'' Jon Lyle Smith</li><li>A number of compositions from [http://www.archive.org/details/seventeenTPP_01 seventeen-tone piano project phase I] , [[SeventeenTPPPhaseTwo|seventeen-tone piano project phase II]], [[SeventeenTPPPhaseThree|seventeen-tone piano project phase III]].</li><li>[http://www.archive.org/search.php?query=subject%3A%2217-edo%22 17edo] - 17edo-tagged compositions on www.archive.org</li><li>[http://soundclick.com/share?songid=8839072 sing a blue] by Andrew Heathwaite (composed 2008, recorded 2010). This and the other pieces below by Andrew for cümbüş, steel tubes &amp; voice.</li><li>[http://soundclick.com/share?songid=8839073 stringfinger it everybean] by Andrew Heathwaite (composed 2008, recorded 2010).</li><li>[http://soundclick.com/share?songid=8839069 cat feet belly] by Andrew Heathwaite (composed 2008, recorded 2010).</li><li><span style="">''[http://www.youtube.com/watch?v=a9N_T6LNDaE 17 Tone Jam]'' </span> by Marmalade Man</li><li>[http://www.youtube.com/results?search_query=17edo&search=tag youtube videos tagged with 17edo]</li><li>[http://chrisvaisvil.com/?p=784 On the Shores of the Dead Sea blog] <span style="">''[http://www.youtube.com/watch?v=D39MVFhb0Ho video of On the Shores of the Dead Sea]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=466 Only in Disneyland 17 blog] edo guitar solo <span style="">''[http://micro.soonlabel.com/17-ET/daily20110205-17et-disneyland.mp3 play Only in Disneyland]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=460 17 Reasons I Hate the Blues blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110125b-17-reasons-I-hate-the-blues.mp3 play 17 Reasons I Hate the Blues]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=422 Klingon Opera Overture blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110109-albino-17et.mp3 play Klingon Opera Overture]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=298 Seventeen Selfless Notes blog] <span style="">''[http://micro.soonlabel.com/17-ET/if20101028selfless.mp3 play Seventeen Selfless Notes]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=76 17ET Jazz blog] <span style="">''[http://micro.soonlabel.com/17-ET/60x60-4001-1-ver2.mp3 play 17et Jazz]'' </span> by Chris Vaisvil (60 x 60 winner)</li><li>[http://chrisvaisvil.com/?p=742 17 Pink Tuxedos blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110416-17_pink-tuxes.mp3 play 17 Pink Tuxedos]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=706 Devil in the Deep Blue Sea blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110401-17-2-devil_in_the_deep_blue_sea.mp3 play Devil in the Deep Blue sea]'' </span> blues collaboration between The Two Regs (vocals / lyrics) and Norm Harris (percussion) and Chris Vaisvil (17 note per octave electric guitar and fretless bass).</li><li>[http://chrisvaisvil.com/?p=585 Seventeen Years in the Sixties blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110318-seventeen-years-in-the-sixties.mp3 play Seventeen Years in the Sixties]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=699 CT Scan blog] <span style="">''[http://www.youtube.com/watch?v=ZEEuytYwtbo play video CT Scan]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=470 Fish and a Grenade blog] <span style="">''[http://micro.soonlabel.com/17-ET/daily20110208-17-a-fish-and-a-grenade.mp3 play Fish and a Grenade]'' </span> (parental advisory language) by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=550 Seventeen Unsteady Hands blog] <span style="">''[http://www.youtube.com/watch?v=rAKHCqBNhfc play video of performance of Seventeen Unsteady Hands]'' </span> by Chris Vaisvil</li><li>[http://chrisvaisvil.com/?p=38 The Pond blog] by Chris Vaisvil and <span style="">''[http://www.youtube.com/watch?v=25sC3_uheyA video version of The Pond with Japanese Garden ]'' </span></li><li><span style="">[http://chrisvaisvil.com/?p=305 Graveyard blog] </span><span style="">''[http://micro.soonlabel.com/17-ET/if20101028-graveyard.mp3 play Graveyard]'' </span> by Chris Vaisvil</li><li><span style="">''[http://micro.soonlabel.com/17-ET/daily20110713_q49_17_brass_voice_choirs.mp3 For Brass and Voice Choirs in 17 edo]'' </span> by [http://chrisvaisvil.com/ Chris Vaisvil ] [http://chrisvaisvil.com/?p=1039 more on the composition]</li><li><span style="">''[http://micro.soonlabel.com/17-ET/daily20111015-fungi.mp3 And I Became One With My Per Fungi]'' </span> by [http://chrisvaisvil.com/ Chris Vaisvil] =&gt; [http://chrisvaisvil.com/?p=1439 more on composition]</li><li><span style="">''[http://micro.soonlabel.com/17-ET/20111014-STE-002-counter-intuitive.mp3 counterintuitive (17 edo guitar solo)]'' </span> by [http://www.chrisvaisvil.com/ Chris Vaisvil] =&gt; [http://chrisvaisvil.com/?p=1427 more on composition]</li><li>[http://micro.soonlabel.com/gene_ward_smith/Others/Sanchez/No_Love_by_Gregory_Sanchez_1_on_SoundCloud___Hear_the_world_s_sounds.mp3 No Love] by [https://soundcloud.com/gregory-sanchez-2/no-love Gregory Sanchez]</li></ul>
[[カテゴリ:17平均律]]
[[カテゴリ:オクターブ平均律‎]]

2024年8月14日 (水) 09:28時点における最新版

← 16平均律17平均律18平均律 →
素因数分解 17（素数）
音程 70.5882¢ 
完全五度 10\17 (705.882¢)
(semiconvergent)
半音比 (A1:m2) 2:1 (141.2¢ : 70.59¢)
一貫限度 3
厳密一貫限度 3

17平均律はオクターブを均等に17分割したものであり、各ステップは約 70.588 ¢ である。13平均律に次ぎ19平均律の前となる、7番目の素数平均律である。

17平均律の音程と近似値

各周波数比の大きさが16以内で表現される純正音程は以下のようになる。これはedjirulerを用いて、[number of equal divisions=17, interval of equivalence=2, integer limit=16, threshold of JI pitch inclusion=0.25]というパラメータで生成したものである。「The “neighborhood” of JI」の一覧はこちら（huygens-fokker）を参照のこと。

EDO interval cent DMS The "neighborhood" of JI Japanese name ratio diff cent cent diff DMS DMS
17 0 0.00 0.00
1 70.59 21.18
2 141.18 42.35 2/3-tone 2/3全音 14/13 12.88 128.30 3.86 38.49
2 141.18 42.35 tridecimal 2/3-tone 13リミットの2/3音 13/12 2.60 138.57 0.78 41.57
2 141.18 42.35 3/4-tone, undecimal neutral second 3/4全音、11リミットの中立的な2度 12/11 -9.46 150.64 -2.84 45.19
3 211.76 63.53 major whole tone 大全音 9/8 7.85 203.91 2.36 61.17
4 282.35 84.71 septimal minor third 7リミットの短3度 7/6 15.48 266.87 4.64 80.06
4 282.35 84.71 tridecimal minor third 13リミットの短3度 13/11 -6.86 289.21 -2.06 86.76
5 352.94 105.88 undecimal neutral third 11リミットの中立3度 11/9 5.53 347.41 1.66 104.22
5 352.94 105.88 tridecimal neutral third 13リミットの中立3度 16/13 -6.53 359.47 -1.96 107.84
6 423.53 127.06 undecimal diminished fourth or major third 11リミットの減4度または長3度 14/11 6.02 417.51 1.81 125.25
6 423.53 127.06 septimal major third, BP third 7リミットの長3度、ボーレン・ピアスの3度 9/7 -11.55 435.08 -3.47 130.53
7 494.12 148.24 perfect fourth 完全4度 4/3 -3.93 498.04 -1.18 149.41
8 564.71 169.41 undecimal semi-augmented fourth 11リミットの準増5度 11/8 13.39 551.32 4.02 165.40
9 635.29 190.59 tridecimal diminished fifth 13リミットの減5度 13/9 -1.32 636.62 -0.40 190.99
9 635.29 190.59 undecimal semi-diminished fifth 11リミットの準減5度 16/11 -13.39 648.68 -4.02 194.60
10 705.88 211.76 perfect fifth 完全5度 3/2 3.93 701.96 1.18 210.59
11 776.47 232.94 septimal minor sixth 7リミットの長6度 14/9 11.55 764.92 3.47 229.47
11 776.47 232.94 undecimal augmented fifth 11リミットの増5度 11/7 -6.02 782.49 -1.81 234.75
12 847.06 254.12 tridecimal neutral sixth 13リミットの中立6度 13/8 6.53 840.53 1.96 252.16
13 917.65 275.29 septimal major sixth 7リミットの長6度 12/7 -15.48 933.13 -4.64 279.94
14 988.24 296.47 Pythagorean minor seventh ピタゴラスの短7度 16/9 -7.85 996.09 -2.36 298.83
15 1058.82 317.65 21/4-tone, undecimal neutral seventh 21/4全音、11リミットの中立7度 11/6 9.46 1049.36 2.84 314.81
15 1058.82 317.65 16/3-tone 16/3全音 13/7 -12.88 1071.70 -3.86 321.51
16 1129.41 338.82
17 1200.00 360.00

理論

17平均理論の導入として、SeventeenTonePianoProject :17音理論に目を通すとよい。もう1つの導入として、George SecorのThe 17-tone Puzzleにも目を通すとよい。17edo Solfege.17平均律テトラコード.Proyect 17-Perúも参照のこと。

平均律は2.3.25.7.11.13サブグループテンペラメントとしてもっともらしく扱うことができる。それはとても計算されている。7リミット周波数比は一般的に、他の整数と同じぐらい良く現れないけども。

素数倍音

17EDOにおける素数倍音の近似
倍音 2 3 5 7 11 13 17 19 23 29 31
誤差 絶対 (¢) +0.0 +3.9 -33.4 +19.4 +13.4 +6.5 -34.4 -15.2 +7.0 +29.2 -15.6
相対 (%) +0.0 +5.6 -47.3 +27.5 +19.0 +9.3 -48.7 -21.5 +9.9 +41.4 -22.1
ステップ
(reduced) 		17
(0) 		27
(10) 		39
(5) 		48
(14) 		59
(8) 		63
(12) 		69
(1) 		72
(4) 		77
(9) 		83
(15) 		84
(16)

純正音程近似

純正音程のマッピング

以下の表は、17平均律で15奇数リミット音程がどのように表されるかを示している。素数倍音は太字で、非一貫的な音程は斜体で示す。

17平均律内の15奇数リミット音程（直接近似, 一貫性の無いものも含む）
音程と補音程 誤差 (絶対, ¢) 誤差 (相対, %)
1/1, 2/1 0.000 0.0
13/9, 18/13 1.324 1.9
13/12, 24/13 2.604 3.7
3/2, 4/3 3.927 5.6
11/9, 18/11 5.533 7.8
11/7, 14/11 6.021 8.5
13/8, 16/13 6.531 9.3
13/11, 22/13 6.857 9.7
9/8, 16/9 7.855 11.1
11/6, 12/11 9.461 13.4
9/7, 14/9 11.555 16.4
13/7, 14/13 12.878 18.2
11/8, 16/11 13.388 19.0
7/6, 12/7 15.482 21.9
7/5, 10/7 17.806 25.2
7/4, 8/7 19.409 27.5
15/14, 28/15 21.734 30.8
11/10, 20/11 23.828 33.8
15/11, 22/15 27.755 39.3
9/5, 10/9 29.361 41.6
15/8, 16/15 29.445 41.7
13/10, 20/13 30.685 43.5
5/3, 6/5 33.288 47.2
5/4, 8/5 33.373 47.3
15/13, 26/15 34.612 49.0
17平均律内の15奇数リミット音程（パテントヴァルによるマッピング）
音程と補音程 誤差 (絶対, ¢) 誤差 (相対, %)
1/1, 2/1 0.000 0.0
13/9, 18/13 1.324 1.9
13/12, 24/13 2.604 3.7
3/2, 4/3 3.927 5.6
11/9, 18/11 5.533 7.8
11/7, 14/11 6.021 8.5
13/8, 16/13 6.531 9.3
13/11, 22/13 6.857 9.7
9/8, 16/9 7.855 11.1
11/6, 12/11 9.461 13.4
9/7, 14/9 11.555 16.4
13/7, 14/13 12.878 18.2
11/8, 16/11 13.388 19.0
7/6, 12/7 15.482 21.9
7/4, 8/7 19.409 27.5
15/8, 16/15 29.445 41.7
5/4, 8/5 33.373 47.3
15/13, 26/15 35.976 51.0
5/3, 6/5 37.300 52.8
13/10, 20/13 39.904 56.5
9/5, 10/9 41.227 58.4
15/11, 22/15 42.833 60.7
11/10, 20/11 46.760 66.2
15/14, 28/15 48.855 69.2
7/5, 10/7 52.782 74.8

コンマをなだらかにする

17平均律のヴァルを ⟨17 27 39 48 59 63] とみなした時、次のリストのコンマをテンパーアウトする。

Comma Monzo Value (Cents) Name 1 Name 2 Name 3
134217728/129140163 | 27 -17 > 66.765 17-Comma
25/24 |-3 -1 2> 70.762 Chromatic semitone Dicot comma
32805/32768 | -15 8 1 > 1.9537 Schisma
64/63 | 6 -2 0 -1 > 27.264 Septimal Comma Archytas' Comma Leipziger Komma
245/243 | 0 -5 1 2 > 14.191 Sensamagic
1728/1715 | 6 3 -1 -3 > 13.074 Orwellisma Orwell Comma
420175/419904 | -6 -8 2 5 > 1.1170 Wizma
99/98 | -1 2 0 -2 1 > 17.576 Mothwellsma
896/891 | 7 -4 0 1 -1 > 9.6880 Pentacircle
243/242 | -1 5 0 0 -2 > 7.1391 Rastma
385/384 | -7 -1 1 1 1 > 4.5026 Keenanisma
525/512 | -9 1 2 1 > 43.408 Avicennma Avicenna's Enharmonic Diesis

メモ：17-comma、avicennma、chromatic semitoneは比較的大きいサイズにもかかわらず、すべて13リミットの特徴的なヴァルによりテンパーアウトされる。

Scales

List of 17edo rank two temperaments by badness

List of edo-distinct 17c rank two temperaments

Music

Compositions

Sound files

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